Originally posted by jspi But I though I'd ask if there's a quick way to figure it out without having to memorize a chart.
No, you just have to memorize. As others have said, it helps to know for "full stops" to start with f/1 and f/1.4 and then double every other f/stop to know the next f/stop.
Shutter speeds get funky and also require memorization because if you start with 1 second, how do we end up at 1/15" instead of 1/16"? And why does it go from 1/60" to 1/125"? In reality the numbers should be 1/16", 1/32", 1/64", 1/128", etc. And have you ever timed a 15" or 30" exposure? Yup, it's really 16" and 32".
As a teacher working with students with some cameras that shoot in increments of 1/2 stops and 1/3 stops, you just have to memorize those numbers. Back in the 20th century, we would call f/6.7 a "split f/5.6-8", because it was some unknown value between the written f/stops. For 1/3 stops, instead of f/6.3 we'd call it a 'hot 5.6" and f/7.1 a 'cool 8'.
And even ISO's are not immune. ISO 50, 100, 200, etc, great! But what's up with ISO 125 and 160 between 100 and 200? Why not 133 and 166?
The brain is an amazing thing, and we got to the moon and back with pencil and paper and slide rulers with some rudimentary help from computers. And I've known cinematographers that never used a light meter and could look at the light and nail the EV as well as a spot meter on an 18% gray card.